Localizing Sources of Network Diffusion via Graph Signal Processing

在过去的十年里，人们对现代社会的复杂连通性越来越着迷。由于对系统级科学分析的普遍兴趣以及各个领域高通量数据收集能力的不断增长，网络的研究随着从物理学到系统工程和生物行为科学等多学科研究的努力而急剧增加。随着现代互联系统在规模和重要性上的增长，它们变得更加复杂和异构，迫切需要提出一种整体网络理论。在此背景下，该项目的研究将有助于理解从关键工程基础设施到大脑的大规模和强耦合系统的固有复杂性。它也将影响网络的教学和设计，以及信号处理的理论和实践在基础层面。在更广泛的范围内，通过该项目网络科学主题的跨领域外推，这里开发的见解和技术将为基础科学和工程研究提供有价值的工具，对环境和经济产生积极影响，并为网络安全、物联网技术、神经科学、医疗保健和网络物理系统的传感集成带来益处。这项研究工作特别强调分布式网络过程的建模、识别和可控性——通常被概念化为在图的顶点上定义的信号。为了解开这些信号的潜在结构，关键的新见解是将它们视为未观察到的图形过滤器的输出，这些过滤器模拟了复杂网络动态的出现。虽然简单，但图过滤器很吸引人，因为它们表示图信号之间的线性变换，可以通过节点之间的局部交互实现，并且它们非常适合建模网络扩散过程，同时保持分析可处理性。在这个方向上，研究议程是开发新的理论和算法，以解决给定观察（输出）图形信号的网络扩散源定位的挑战性问题，例如，由无线传感器网络测量的空间温度曲线，社交网络中的意见曲线，或大脑不同区域的神经活动。在基本层面上，这项工作将经典的盲系统识别扩展到网络，或者将时空信号的盲反卷积扩展到非结构化图域。提倡图形信号处理方法的目的是提高对该领域的兴趣，超越其作为经典信号处理的优雅概括的理论美学，并强调其在解决与传感器，社会和大脑网络等遇到的现实世界工程问题时的实际意义。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Localizing Sources of Network Diffusion via Graph Signal Processing Over the past decade there has been a growing fascination with the complex connectedness of modern society. As a result of the pervasive interest in scientific analysis at a system level along with the ever-growing capabilities for high-throughput data collection in various fields, the study of networks has increased dramatically with multidisciplinary research efforts from researchers ranging from physics to systems engineering and the bio-behavioral sciences. As modern interconnected systems grow in size and importance, while they become more complex and heterogeneous, there is an urgent need to advance a holistic theory of networks. In this context, research in this project will contribute towards understanding the inherent complexities of large-scale and strongly coupled systems ranging from critical engineering infrastructures to the brain. It will also impact teaching and design of networks, as well as signal processing theory and practice at the fundamental level. At a broader scale, through cross-domain extrapolation of this project's Network Science leitmotif, the insights and technologies developed here will provide valuable tools for fundamental science and engineering research, positively impact environment and economy, and permeate benefits to cyber-security, IoT technologies, neuroscience, healthcare and sensing-integration for cyber-physical systems.This research effort places particular emphasis on modeling, identification, and controllability of distributed network processes - often conceptualized as signals defined on the vertices of a graph. To untangle the latent structure of such signals, the key novel insight is to view them as outputs of unobserved graph filters that model the emergence of complex network dynamics. Albeit simple, graph filters are appealing since they represent linear transformations between graph signals that can be implemented via local interactions among nodes, and they are well-suited to model network diffusion processes while remaining analytically tractable. In this direction, the research agenda is to develop novel theory and algorithms for the challenging problem of localizing sources of network diffusion given an observed (output) graph signal, e.g., a spatial temperature profile measured by a wireless sensor network, an opinion profile in a social network, or the neural activity in different regions of the brain. At a fundamental level, this effort broadens the scope of classical blind system identification to networks, or, of blind deconvolution of temporal and spatial signals to unstructured graph domains. Advocating a graph signal processing approach the aim tis o boost the interest in the area beyond its theoretical aesthetics as an elegant generalization of classical signal processing, and highlight its practical implications when solving real-world engineering problems encountered with sensor, social and brain networks, to name a few.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.